Question

If x-1/x = 9 find the value of x +1/x

Answer 1

Answer:

$\sqrt{85}$

Step-by-step explanation:

Given

x - $\frac{1}{x}$ = 9 ← square both sides

(x - $\frac{1}{x}$)² = 9²

x² - 2 + $\frac{1}{x^2}$ = 81 ( add 2 to both sides )

x² + $\frac{1}{x^2}$ = 83

Now

(x + $\frac{1}{x}$)² = x² + $\frac{1}{x^2}$ + 2, thus

x² + $\frac{1}{x^2}$ = 83 + 2 = 85

(x + $\frac{1}{x}$ )²= 85 ( take the square root of both sides)

x + $\frac{1}{x}$ = $\sqrt{85}$